Synaptically Seductive Sequence: Meditations on Math, Mysticism, Metaphysics, Masculinity, Melanin and Morality

Almost everyone has a favorite number. So if you aspire higher than the herd, you need a favorite number-sequence too. In fact, you need lots of them. Here’s one of mine:

1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, …

See if you can work out the rule self-generating the sequence. If you can, congratulations. If you can’t, don’t worry. The Kolakoski sequence, as it’s known, is simultaneously supremely simple and synapse-seducingly subtle. On the one hand, it’s entirely deterministic; on the other, it’s uncannily unpredictable. It’s merely mathematical, it’s mundanely mechanical, but it seems to have a mind of its own. Technically speaking, the Kolakoski sequence is identical to its own run-length encoding. In other words, if you write down the lengths of the runs of 1 and 2, you reproduce the same sequence [see Note 1]. This means that the Kolakoski sequence consists of nothing but 1s and 2s in runs of one and two.

William Kolakoski and his synaptically seductive sequence (adapted self-portrait from Wikipedia)

As I said: supremely simple. And mathematicians have been studying this supremely simple sequence for decades. But they’ve never found a straightforward formula for an arbitrary entry in the sequence. That is, no-one can easily tell in advance whether the 100th or 1000th or 1,000,000th number in the sequence is 1 or 2. To know that, it can be quicker to work out everything that comes before. In short, the sequence isn’t periodic and isn’t predictable. And no-one can yet prove that 1s occur there as often as 2s. As I also said: synapse-seducingly subtle.

Strangely beautiful

The sequence certainly seduced the synapses of the man who gave it his name. It soothed his synapses too. This was because William Kolakoski (1944-97), the American artist and amateur mathematician who popularized the sequence in 1965, was schizophrenic and needed constant medication to prevent his mind being carried into what a friend of his called “regions of chaos and delusion.” Because he couldn’t control his own brain, Kolakoski felt compelled to reject free will and accept determinism. But he wanted to find some “benevolent order” in the deterministic universe and he believed that his sequence was one expression of it. As I noted above, the Kolakoski sequence is entirely deterministic, but uncannily unpredictable. It’s also strangely beautiful. Discussions of it on the web sometimes make the claim that it’s “the only sequence” that is its own run-length encoding. That isn’t just wrong, but infinitely wrong. There are an infinite number of such sequences:

1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 3, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, 3, 1, 3, 3, 3, 1, 1, 1, 3, 3, 3, 1, … (Kolakoski sequence using 1,3)

2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 2, … (Kolakoski sequence using 2,3)

1, 2, 2, 3, 3, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 1, 2, 3, 4, 4, 1, 1, 2, 2, 3, 3, 4, 4, 4, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, … (Kolakoski sequence using 1,2,3,4)

If someone’s synapses aren’t seduced by such sequences, then they’ll never enter nerd-nirvana. But if their synapses are seduced, I can make two confident predictions about them. First, they’re probably male. Second, they’re probably light-skinned. They’re White or Jewish or Asian, not Black in the fullest, melanin-tastickest sense. Math appeals most to pale stale males like William Kolakoski. And like Rufus Oldenburger (1908–69), the American mathematician who first published the sequence in 1945.² But that year is very late in the history of mathematics. Why was such a simple and seductive sequence not discovered millennia ago? That’s an interesting question. It’s also interesting to speculate what would happen to intellectual history if we could use a time-machine to teach Pythagoras or Archimedes or Aryabhata about the sequence.

All of those mathematical giants would have found their synapses seduced by it, I think.³ But Pythagoras might have been seduced most of all. After all, he was a mystic and metaphysician as well as a mathematizer. The Kolakoski sequence is mystically and metaphysically mesmerizing as well as mathematically so. As I said above: it seems to have a mind of its own. Indeed, a life of its own. The Fibonacci sequence – 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … – famously illuminates biology.⁴ The Kolakoski sequence almost seems to belong to biology. What would Pythagoras have made of it? I think he would have been dazzled and delighted by it. And if the Kolakoski sequence had become part of early mathematics, it might have profoundly altered and enriched the course and content of the field. Perhaps calculus would have appeared centuries or millennia earlier, and not had to wait for the genius of those two pale stale males Isaac Newton (1642–1726) and Gottfried Leibniz (1646–1716).

The geometry of life

Why Newton and Leibniz didn’t discover the Kolakoski sequence is a question that currently belongs to history and the philosophy of mathematics. Why they did discover calculus is a question that now belongs partly to biology, because their genius is explained by something else that Pythagoras would have been dazzled and delighted by, namely, DNA. Part of his delight would have come from a sense of vindication. Pythagoras believed that “Number rules the Universe.” DNA is, in effect, a number-sequence that rules all earthly life. In other words, biology is mathematics: Aei hē Zoē geōmetreî, “Life eternally geometrizes,” as Plato might have put it.⁵ That ancient Greek verb, geōmetreî, captured the modern sense of “do mathematics” because Greek mathematics centered on geometry.

DNA would have dazzled and delighted Pythagoras

But DNA geometrizes in a more literal sense. It’s a geometric embodiment of a number-sequence, because the physical structure of DNA — its geometry — explains how it works, how it encodes and directs the manufacture of proteins. DNA is a splittable spiral, a double helix whose structure and simplicity would have added to the dazzlement and delight of Pythagoras. Biology is mathematics and mechanics! In effect, a human body is a giant factory full of microscopic machines manufacturing and maintaining meat. And also manufacturing and maintaining mind. Whatever the precise nature and origin of consciousness, there can be no doubt that it is profoundly influenced by mindless matter and by those microscopic machines of DNA. In some sense, mind is both mechanical and mathematical. If we want to explain the very wide mental variation among humans, we have to understand the mechanics and mathematics of DNA.

“A hidden arithmetic of the soul”

That’s because DNA governs the differing psychology and cognition of different human races. Indeed, DNA explains why and how there are different human races. DNA has mutated in the course of human history and now differs in significant ways from race to race, just as DNA has mutated in deeper biological time and differs from male to female. This produces a delicious irony: the number-sequence of DNA explains why some human beings delight in number-sequences and some don’t. And why some human beings are much better at understanding and manipulating number-sequences, in both a narrow and a wide sense. The great philosopher Leibniz, co-creator of calculus, once wrote that Musica exercitium arithmeticae occultum nescientis se numerare animi – “music is a hidden arithmetic exercise of the soul, unaware that it calculates.” In other words, music is mathematics (and is another synapse-seducing sequence). It’s not a coincidence that perhaps the greatest mathematician of all time, Carl Friedrich Gauss (1777–1855), belonged to the same race as perhaps the greatest composer of all time, Ludwig van Beethoven (1770–1827). Leibniz, a GOAT in both philosophy and mathematics, belonged to that race too.

Charles Murray’s hate-hexagon captures 97% of human accomplishment by stale pale males in Europe

It was the German branch of the White European race. Gauss, Beethoven and Leibniz were all pale stale males. So, in a wider sense, is perhaps the greatest living mathematician, the Chinese Terry Tao (born 1975). He’s perhaps the greatest on Earth, that is, but there may be far greater mathematicians elsewhere in the Universe, members of alien species with radically different biologies. In one sense, math floats free of biology: it’s presumably a universal language for advanced intelligent beings of any kind, which is why we’ve beamed prime numbers at the stars to prove our existence and intelligence, not the poetry of Maya Angelou. But in other senses math is closely bound to biology. The Fibonacci sequence is one famous example. It governs the structure of pine-cones and pineapples, yet those species are subjects of math, not sovereigns of it like Homo sapiens. You could say that pine-cones and pineapples are mathematics, that is, they embody mathematics. Human beings both are mathematics and do mathematics.⁶ And if you want to understand why, you have to understand the biology of human beings and the number-sequence of their DNA.

Misomathematical mysticism

More specifically, you have to understand the biology of those individuals and races who invented and excel at mathematics. As I pointed out above, the individuals have a strong tendency to be pale stale males, from Pythagoras in the 6th century before Christ to Terry Tao in the twenty-first century after. The maximal masculinity of math is explained by the evolution of males to hunt and hurl weapons;⁷ the minimal melanicity of math is explained by the evolution of higher intelligence at higher latitudes in colder climates. In other words, the mathematics of DNA explains why some human beings have a mind for mathematics and some don’t. DNA is mechanically mathematical (and vice versa). But mystics, of course, object to the mechanization and mathematization of mind. There’s a great irony in that misomathematical mysticism, because some of those who espouse it are followers of a man who would, like Pythagoras, have been dazzled and delighted by DNA. And like Pythagoras he would have felt vindicated by it. But whereas Pythagoras would have hailed the mathematicality of DNA, Karl Marx (1818–83) would have hailed the materiality of DNA.

Marxism in its classic form claims to be a strictly materialist ideology. But modern Marxists, like the wider, Marx-influenced left in general, are resolutely anti-material when it comes to race and the influence of mere DNA on the majesty of mind. They deny the existence of race and claim that only sociology, not biology, can explain why Black women, for example, haven’t scaled the heights of mathematics like the stale pale males Isaac Newton and Terry Tao. For example, their devotion to Marxism unites stale pale males like Stephen Jay Gould, Richard Lewontin, Leon Kamin, and Steven Rose, the most important and influential of the DNA-deniers. They are all adherents of a strictly materialist ideology. And yet they resort to mysticism when it comes to racial and sexual difference, denying that genetics can explain the vastly different behavior and achievements of Whites and Blacks or men and women.

Partisan, not impartial

However, something else unites these dominant DNA-deniers. They are also all Jewish. So are the DNA-deniers — with delicious irony — determined by DNA? I would say yes, to some degree at least. Jewish DNA certainly accounts for the intelligence and verbal facility of Gould, Lewontin et al. Scholars like Kevin MacDonald would further claim that Jewish DNA accounts for the ethnocentrism of the Gouldeans, who haven’t been impartial scientists pursuing truth but partisan ideologues pursuing Jewish advantage. It’s not good for Jews for Whites to recognize the simple truth, namely, that biology underlies behavior and that the failure of Blacks in Western societies has deep genetic and evolutionary roots. But it is good for Jews for Whites to embrace a gigantic lie, namely, that sociology is supreme and that all non-White failure can be blamed on White racism. The Gouldeans are mendacious, not Mendelian. So you could also say they are immoral. And I would say that DNA also profoundly influences morality: some races have evolved for deceit and manipulation, and even for straightforward criminality.

As I pointed out in my article “Verbal Venom,” predation and parasitism have spontaneously evolved again and again in the animal kingdom. There are parasitic mammals, birds, fish, insects and more: Think of vampire-bats, cuckoos, lampreys, mosquitoes and so on. All of those animal groups behave in what is, from one perspective, a profoundly immoral way. They steal the hard-earned resources of their fellow creatures, deceiving and manipulating and sometimes literally sucking their blood. But morality doesn’t really apply, of course. It’s biology, not badness, that’s at work when a mosquito sucks human blood or a cuckoo-chick flips its unrelated nest-mates to their death and then exploits the labor of the deceived parents. And I think it’s biology, not badness, if those same readily evolving strategies of predation and parasitism have appeared among human beings. Predation and parasitism are written into mosquito and cuckoo DNA and may also be written into the DNA of some human groups.

Genetic geometry shows that Jews are distinct from northern European Whites

But DNA is a number-sequence, not a code of ethics. Morality dissolves in mathematics. I don’t think we can blame Stephen Jay Gould for his anti-Mendelian mendacity. As Kevin MacDonald points out, Gould proclaimed this in his most famous book, The Mismeasure of Man (1996): “May I end up next to Judas Iscariot, Brutus, and Cassius in the devil’s mouth at the center of hell if I ever fail to present my most honest assessment and best judgment of the evidence for empirical truth.” That was self-righteous and Gould is self-damned, because The Mismeasure of Man is replete with mendacity. But if Gould denied scientific truth and MacDonald champions it, that divergence isn’t surprising. Both men belong to small human groups that have had a vastly disproportionate influence on the world. But Scots, who have mostly had a good influence, are White and Jews, who have often had a bad influence, are not. Analysis of DNA has proved that. The three-dimensional geometry of DNA can be translated into a two-dimensional geometry of gene-clusters.⁸ On a gene-cluster map, Jews stand as a people alone, separated by the Southern-European cluster from Scots in the Northern-European cluster. But there’s another irony in such mathematically based DNA analysis, because one of the central figures in the discovery of DNA’s geometry was much more closely related to Stephen Jay Gould than she was to two of the other central figures in the DNA story.

James Watson (born 1928) and Francis Crick (1916-2004) were White like Kevin MacDonald, but the X-ray crystallographer Rosalind Franklin (1920–58) was Jewish like Stephen Jay Gould.⁹ Unlike Gould, she was a true scientist, but unlike Crick and Watson she never achieved the scientific immortality of a Nobel prize. She died too soon and perhaps being a woman during her lifetime would have denied her a Nobel anyway. Immortality can be much easier to achieve in mathematics. William Kolakoski died young like Franklin, but he achieved immortality by discovering and giving his name to that synaptically seductive sequence of 1, 2, 2, 1, 1, 2, 1, 2, 2…

Or rather: by re-discovering it. Rufus Oldenburger was there first. Or first on Earth, at least. Perhaps the Kolakoski sequence was first discovered millennia ago and light-years away by an alien being with a radically different biology. As I pointed out above, in one sense math floats free of biology. But, as I also pointed out above, in other senses math is closely bound to biology. I myself wish I were much better at it. Then again, I can boast that I’m very good at it already, like almost every human since the number-sequence of DNA first granted us the faculty of speech. Whether it’s spoken or written, language too is a number-sequence. It isn’t turtles all the way down, it’s numbers and algorithms and math. Le monde, c’est mathématique.¹⁰

Notes

1. “How to generate the sequence

   The Kolakoski Sequence … is a self-describing sequence. The sequence consists of only 1s and 2s, and begins with 1. Each term in the sequence describes the length of the next run of the same number (either 1s or 2s). That probably didn’t make sense (as it didn’t to me the first time I read it), so let me show you what I mean…
   The sequence begins with 1. So this means the first run of the same digit only contains 1 number. Since the first number is 1, this means there must only be one 1 in this run. And by definition, because this run must only contain one 1, the next number must be 2.
   Because the second number is 2, that means that there are 2 of the same number in the next run. So the sequence will next contain another 2. And this term will be the end of this run of the same number.
   Because the third term is 2, we know that the next run of the same number will have length 2. Because we know the third term was the end of the last run, the fourth term has to be 1.
   The fifth term will also be 1, as this run has to have length 2.”

   You can also create the Kolakoski sequence by dropping the initial 1 like this: 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, …

2. Oldenburger’s precedence means that the Kolakoski sequence is an example of Stigler’s law of eponymy, which states that “no scientific discovery is named after its original discoverer.” Stigler’s law is also, by design, an example of Stigler’s law.
3. Of course, if a time-machine took the Kolakoski sequence back in time, there would be no need for a time-machine to take the Kolakoski sequence back in time. You can avoid this paradox by invoking the multiverse and supposing that a time-machine from one universe hops across to another universe that’s accessible and observable from the former.
4. For example, as noted later in the article, the Fibonacci sequence helps explain the structure of pine-cones and pineapples.
5. According to Plutarch, Plato believed that ἀεὶ ὁ Θεὸς γεωμετρεῖ, aei ho Theos geōmetreî, “God ever geometrizes.”
6. That is, we humans are governed in our biology, physiology, etc by mathematical principles, but are also capable of creating and performing mathematics as an explicit symbology.
7. Tracking prey involves following a sequence of spoor through space; throwing spears or firing arrows selects for spatial ability too.
8. In fact, gene-space has far more dimensions than two, but the gene-cluster map above uses only two and I’m simplifying for rhetorical effect.
9. And like the mathematical giant Emmy Noether (1882–1935). As I noted above, stale pale males have dominated math, but stale pale females have sometimes been important there too.
10. “The world, it’s mathematical.” After the manically alliterative title of this article, that’s a mildly alliterative envoi in French (inspired by Louis XIV’s alleged remark L’etat, c’est moi, “I am the state”). Perhaps both the mania and the mildness can be explained by my genetics. Anglo-Saxon poetry was famously based on alliteration, not on rhyme. Gene-expression strengthens with age and the older I’ve got, the more I’ve felt compelled to alliterate. I hope this sequence about a synaptically seductive sequence has been synaptically seductive in its own written right.